On the Existence and Nonexistence of Splitter Sets
Abstract
In this paper, the existence of perfect and quasi-perfect splitter sets in finite abelian groups is studied, motivated by their application in coding theory for flash memory storage. For perfect splitter sets we view them as splittings of $\mathbb{Z}_n$, and using cyclotomic polynomials we derive a general condition for the existence of such splittings under certain circumstances. We further establish a relation between $B[-k, k](q)$ and $B[-(k-1), k+1](q)$ splitter sets, and give a necessary and sufficient condition for the existence of perfect $B[-1, 5](q)$ splitter sets. Finally, two nonexistence results for quasi-perfect splitter sets are presented.
Fields of Study & Subjects
Cellular Automata and Applications
graph theory and CDMA systems
Limits and Structures in Graph Theory
Publication details
- Journal / source
- IEEE Transactions on Information Theory
- Volume
- 72
- Issue
- 10
- Pages
- 7359–7370
- Publication date
- 22 July 2026
- Language
- EN